The matrix M is defined asand has eigenvalues 5and andminus;2. The matrix Qis formed as Q = M3- 4M2- 2MWhich of the following is/are the eigenvalue(s) of matrix Q?a)15b)25c)-20d)-30Correct answer is option 'A,C'. Can you explain this answer?

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The matrix M is defined as

and has eigenvalues 5 and −2. The matrix Q is formed as Q = M³ - 4M² - 2M
Which of the following is/are the eigenvalue(s) of matrix Q?

a)
15
b)
25
c)
-20
d)
-30

Correct answer is option 'A,C'. Can you explain this answer?

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The matrix M is defined asand has eigenvalues 5and −2. The matri...

Properties of eigenvalues-

Eigenvalues of unitary and orthogonal matrices are of unit modulus |λ| = 1

If λ1, λ2…….λn are the eigenvalues of A, then kλ1, kλ2…….kλn are eigenvalues of kA
If λ1, λ2…….λn are the eigenvalues of A, then 1/λ1, 1/λ2…….1/λn are eigenvalues of A-1
If λ1, λ2…….λn are the eigenvalues of A, then λ1k, λ2k…….λnk are eigenvalues of Ak

Eigenvalues of A = Eigen Values of AT (Transpose)

Sum of Eigen Values = Trace of A (Sum of diagonal elements of A)

Product of Eigen Values = |A|

Maximum number of distinct eigenvalues of A = Size of A

Calculation:

The given eigenvalues are 5 and −2.

Q = M3 - 4M2 - 2M

Eigen values of M³ are 125 and -8,4M² are 100 and 16, 2M are 10 and -4.

SO eigen values of Q, λ1= 125-100-10 = 15,λ2 = -8-16-(-4)=-20

So the eigen values are 15 and -20

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The matrix M is defined asand has eigenvalues 5and −2. The matrix Qis formed as Q = M3- 4M2- 2MWhich of the following is/are the eigenvalue(s) of matrix Q?a)15b)25c)-20d)-30Correct answer is option 'A,C'. Can you explain this answer?

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The matrix M is defined asand has eigenvalues 5and −2. The matrix Qis formed as Q = M3- 4M2- 2MWhich of the following is/are the eigenvalue(s) of matrix Q?a)15b)25c)-20d)-30Correct answer is option 'A,C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The matrix M is defined asand has eigenvalues 5and −2. The matrix Qis formed as Q = M3- 4M2- 2MWhich of the following is/are the eigenvalue(s) of matrix Q?a)15b)25c)-20d)-30Correct answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The matrix M is defined asand has eigenvalues 5and −2. The matrix Qis formed as Q = M3- 4M2- 2MWhich of the following is/are the eigenvalue(s) of matrix Q?a)15b)25c)-20d)-30Correct answer is option 'A,C'. Can you explain this answer?.

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